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  • Author or Editor: N. J. Groenewald x
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A class K of rings has the GADS property (i.e., generalized ADS property) if wheneverX& I& R with X K , then there exists B & R with B K such that XBI. Radicals whose semisimple classes have the GADS property are called g-radicals. In this paper, we fully characterize the class of g -radicals. We show that ? is a g-radical if and only if either ? ⊆ I or S ? ⊆ I , where I denotes the class of idempotent rings and S ? denotes the semisimple class of ?. It is also shown that the (hereditary) g-radicals form an (atomic) sublattice of the lattice of all radicals.

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